. . . most of what we conceive is possible. So if we say that
1) In 80% of the cases, if 'Conceivably, p' then 'Possibly, p' 2) Conceivably, God exists Ergo, 3) Pr(Possibly, God exists) = 80% 4) If 'Possibly, God exists' then 'necessarily, God exists' Ergo, 5) Pr(Necessarily, God exists) = 80%,
we seem to get by.
I had made the point that conceivability does not entail possibility. Hart agrees with that, but seems to think that conceivability is nondemonstrative evidence ofpossibility. Accordingly, our ability to conceive (without contradiction) that p gives us good reason to believe that p is possible.
What is puzzling to me is how a noncontingent proposition can be assigned a probability less than 1. A noncontingent proposition is one that is either necessary or impossible. Now all of the following are noncontingent:
God exists Necessarily, God exists Possibly, God exists God does not exist Necessarily, God does not exist Possibly, God does not exist.
I am making the Anselmian assumption that God (the ens perfectissimum, that than which no greater can be conceived, etc.) is a noncontingent being. I am also assuming that our modal logic is S5. The characteristic S5 axiom states that Poss p --> Nec Poss p. S5 includes S4, the characteristic axiom of which is Nec p --> Nec Nec p. What these axioms say, taken together, is that what's possible and necessary does not vary from possible world to possible world.
Now Possibly, God exists, if true, is necessarily true, and if false, necessarily false. (By the characteristic S5 axiom.) So what could it mean that the probability of Possibly, God exists is .8? I would have thought that the probability is either 1 or 0. the same goes for Necessarily, God exists. How can this proposition have a probability of .8? Must it not be either 1 or 0?
Now I am a fair and balanced guy, as everyone knows. So I will deploy the same reasoning against the atheist who cites the evils of our world as nondemonstrative evidence of the nonexistence of God. I don't know what it means to say that it is unlikely that God exists given the kinds and quantities of evil in our world. Either God exists necessarily or he is impossible (necessarily nonexistent). How can you raise the probability of a necessary truth? Suppose some hitherto unknown genocide comes to light, thereby adding to the catalog of known evils. Would that strengthen the case against the existence of God? How could it?
To see my point consider the noncontingent propositions of mathematics. They are all of them necessarily true if true. So *7 + 5 = 12* is necessarily true and *7 + 5 = 11* is necessarily false. Empirical evidence is irrelevant here. I cannot raise the probability of the first proposition by adding 7 knives and 5 forks to come up with 12 utensils. I do not come to know the truth of the first proposition by induction from empirical cases of adding. It would also be folly to attempt to disconfirm the second proposition by empirical means.
If I can't know that 7 + 5 = 12 by induction from empirical cases, how can I know that possibly, God exists by induction from empirical cases of conceiving? The problem concerns not only induction, but how one can know by induction a necessary proposition. Similarly, how can I know that God does not exist by induction from empirical cases of evil?
Of course, *God exists* is not a mathematical proposition. But it is a noncontingent proposition, which is all I need for my argument.
Finally, consider this. I can conceive the existence of God but I can also conceive the nonexistence of God. So plug 'God does not exist' into Matt's argument above. The result is that probability of the necessary nonexistence of God is .8!
My conclusion: (a) Conceivability does not entail possibility; (b) in the case of noncontingent propositions, conceivability does not count as nondemonstrative evidence of possibility.
After leaving the polling place this morning, I headed out on a sunrise hike over the local hills whereupon the muse of philosophy bestowed upon me some good thoughts. Suppose we compare a modal ontological argument with an argument from evil in respect of the question of evidential support for the key premise in each. This post continues our ruminations on the topic of contingent support for noncontingent propositions.
A Modal Ontological Argument
'GCB' will abbreviate 'greatest conceivable being,' which is a rendering of Anselm of Canterbury's "that than which no greater can be conceived." 'World' abbreviates 'broadly logically possible world.'
1. The concept of the GCB is either instantiated in every world or it is instantiated in no world.
2. The concept of the GCB is instantiated in some world. Therefore:
3. The concept of the GCB is instantiated.
This is a valid argument: it is correct in point of logical form. Nor does it commit any informal fallacy such as petitio principii, as I argue in Religious Studies 29 (1993), pp. 97-110. Note also that this version of the OA does not require the controversial assumption that existence is a first-level property, an assumption that Frege famously rejects and that many read back (with some justification) into Kant. (Frege held that the OA falls with that assumption; he was wrong: the above version is immune to the Kant-Frege objection.)
(1) expresses what I will call Anselm's Insight. He appreciated, presumably for the first time in the history of thought, that a divine being, one worthy of worship, must be noncontingent, i.e., either necessary or impossible. I consider (1) nonnegotiable. If your god is contingent, then your god is not God. There is no god but God. End of discussion. It is premise (2) -- the key premise -- that ought to raise eyebrows. What it says -- translating out of the patois of possible worlds -- is that it it possible that the GCB exists.
Whereas conceptual analysis of 'greatest conceivable being' suffices in support of (1), how do we support (2)? Why should we accept it? Some will say that the conceivability of the GCB entails its possibility. But I deny that conceivability entails possibility. I won't argue that now, though I do say something about conceivability here. Suppose you grant me that conceivability does not entail BL-possibility. You might retreat to this claim: It may not entail it, but it is evidence for it: the fact that we can conceive of a state of affairs S is defeasible evidence of S's possibility.
Please note that Possibly the GCB exists -- which is logically equivalent to (2) -- is necessarily true if true. This is a consequence of the characteristic S5 axiom of modal propositional logic: Poss p --> Nec Poss p. ('Characteristic' in the sense that it is what distinguishes S5 from S4 which is included in S5.) So if the only support for (2) is probabilistic or evidential, then we have the puzzle we encountered earlier: how can there be probabilistic support for a noncontingent proposition? But now the same problem arises on the atheist side.
An Argument From Evil
4. If the concept of the GCB is instantiated, then there are no gratuitous evils.
5. There are some gratuitous evils. Therefore:
6. The concept of the GCB is not instantiated.
This too is a deductive argument, and it is valid. It falls afoul of no informal fallacy. (4), like (1), is nonnegotiable. Deny it, and I show you the door. The key premise, then, the one on which the soundness of the argument rides, is (5). (5) is not obviously true. Even if it is obviously true that there are evils, it is not obviously true that there are gratuitous evils.
In fact, one might argue that the argument begs the question against the theist at line (5). For if there are any gratuitous evils, then by definition of 'gratuitous' God cannot exist. But I won't push this in light of the fact that in print I have resisted the claim that the modal OA begs the question at its key premise, (2) above.
So how do we know that (5) is true? Not by conceptual analysis. If we assume, uncontroversially, that there are some evils, then the following logical equivalence holds:
7. Necessarily, there are some gratuitous evils iff the GCB does not exist.
Left-to-right is obvious: if there are gratuitous evils, ones for which there is no justification, then a being having the standard omni-attributes cannot exist. Right-to-left: if there is no GCB and there are some evils, then there are some gratuitous evils. (On second thought, R-to-L may not hold, but I don't need it anyway.)
Now the RHS, if true, is necessarily true, which implies that the LHS -- There are some gratuitious evils -- is necessarily true if true.
Can we argue for the LHS =(5)? Perhaps one could argue like this (as one commenter suggested in an earlier thread): If the evils are nongratuitous, then probably we would have conceived of justifying reasons for them. But we cannot conceive of justifying reasons. Therefore, probably there are gratuitous evils.
But now we face our old puzzle: How can the probability of there being gratuitous evils show that there are gratuitous evils given that There are gratuitous evils, if true, is necessarily true?
We face the same problem with both arguments, the modal OA for the existence of the GCB, and the argument from evil for the nonexistence of the GCB. The key premises in both arguments -- (2) and (5) -- are necessarily true if true. The only support for them is evidential from contingent facts. But then we are back with our old puzzle: How can contingent evidence support noncontingent propositions?
Neither argument is probative and they appear to cancel each other out. Sextus Empiricus would be proud of me.
In an earlier thread James Anderson makes some observations that cast doubt on the standard entailment from inconceivability to impossibility. (I had objected that his theological mysterianism seems to break the inferential link connecting inconceivability and impossibility.) He writes,
But even though we have no direct epistemic access to any other inconceivability than our own, and despite the formidable historical pedigree of the idea, it still strikes me as implausible to maintain that inconceivability to us entails impossibility. [. . .] For the principle in question is logically equivalent to the principle that possibility entails conceivability. But is it plausible to think that absolutely whatsoever happens to be possible in this mysterious universe and beyond must be conceivable to the human mind, at least in principle? Can this really be right?
I want to emphasize that I'm not advocating some form of modal skepticism, i.e., the view that our intuitions as to what is possible or impossible are generally unreliable. On the contrary, I think they're reliable. I just deny that they're infallible.
This does indeed give me pause. Anderson is certainly right that if inconceivability entails impossibility, then, by contraposition, possibility entails conceivability. These entailments stand or fall together. But is it plausible to maintain that whatever is possible is conceivable? Why couldn't there be possible states of affairs that are inconceivable to us?
But there may be an ambiguity here. I grant that there are, or rather could be, possible states of affairs that we cannot bring before our minds. These would be states of affairs that we cannot entertain due to our cognitive limitations. But that is not to say that a state of affairs that I can bring before my mind and in which I find a logical contradiction is a possible state of affairs. Thus we should distinguish two senses of inconceivable, where S is a state of affairs and A is any well-functioning finite cognitive agent:
S is inconceivable1 to A =df A entertains S and finds a contradiction in S.
S is inconceivable2 to A =df A is unable to entertain (bring before his mind) S.
Now it seems clear that inconceivability2 does not entail impossibility. But I should think that inconceivability1 does entail impossibility. For if S is contradictory, then that very state of affairs as the precise accusative of my thought that it is, cannot obtain. Its possibility in reality is ruled out by the fact that it cannot be entertained without contradiction.
Now does possibility entail conceivability? No, in that the possible need not be thinkable by us: there could be possibilities that lie beyond our mental horizon. But possibility does entail conceivability if what we mean is that possible states of affairs that we can bring before our minds must be free of contradiction.
So, in apparent contradiction to what Anderson is claiming, I urge that we can be infallibly sure that a state of affairs in which we detect a logical contradiction cannot obtain in reality. There is more to reality, including the reality of the merely possible, than what we can think of; but what we can think of must be free of contradiction if it is to be possible.
Conceivability without contradiction is no infallible guide to possibility. But inconceivability1 is an infallible guide to impossibility. Where Anderson apparently sees symmetry, I uphold the traditional asymmetry.
My disembodied existence is conceivable (thinkable without apparent logical contradiction by me and beings like me). But does it follow that my disembodied existence is possible? Sydney Shoemaker floats the suggestion that this inference is invalid, resting as he thinks on a confusion of epistemic with metaphysical possibility. (Identity, Cause, and Mind, p. 155, n. 13.) Shoemaker writes, "In the sense in which I can conceive of myself existing in disembodied form, this comes to the fact that it is compatible with what I know about my essential nature . . . that I should exist in disembodied form. From this it does not follow that my essential nature is in fact such as to permit me to exist indisembodied form."
We need to think about the relation between conceivability and epistemic possibility if we are to get clear about the inferential link, if any, between conceivability and metaphysical possibility. Pace Shoemaker, I will suggest that the inference from conceivability to metaphysical possibility need not rest on a confusion of epistemic with metaphysical possibility. But it all depends on how we define these terms.